Gr. 12 Technical Mathematics
Term 2 - 2024
Paper 1
Total:160 marks Time:2 hours
Learner's name: ________________________________ Gr. 12: __________.
Instructions and information:
This paper consists of five questions, answer all the questions.
You may use a non-programmable and non-graphing calculator.
No Tip – Ex may be used
Show all the steps needed to arrive at the answer.
Good luck!!
Topics covered in this test:
Factoring and solving quadratic equations
Solving linear and non-linear systems of equations
Rearranging formulas
Calculating inductance in an RCL circuit
Conversion between decimal and binary numbers
Quadratic Functions
Nature of Roots
Equal Roots
Simplification and Logarithms
Graphs and Functions
Financial Mathematics
Calculus
Polynomial Functions
Chemical Reaction and Temperature
Integration
1|Page www.summariessa.co.za Technical Math
Grade 12 June Paper 1
,QUESTION 1
1.1 Solve for x
1.1.1 ( 7−3 x ) (−8−x )=0 (2)
2 1
1.1.2 3 x −4 x = (Correct to two decimal places) (4)
3
1.1.3 −x 2+ 16>0 (3)
1.2 Solve for x and y if:
x− y =1 and x +2 xy + y 2 =9 (6)
1.3 In the diagram below shows an RCL circuit used for voltage magnification. The formula to
determine the resonat frequency ( f ¿ of an RCL circuit is given below.
1
f r=
2 π √ LC
Where:
f r=¿resonant frequency in Hz (hertz)
L=¿ inductance in H (henry)
C = capacitance in F (farad)
1.3.1 Make L the subject if the formula. (3)
1.3.2 Hence, calculatee the numerical value of L if C=0.65 ×10−6 F and
f r=1.59 Hz .
(2)
1.4 Express 24 as a binary number. (1)
1.5 Evaluate 144 ÷ 1102 and leave your answer as a decimal number. (2)
[23]
2|Page www.summariessa.co.za Technical Math
Grade 12 June Paper 1
, QUESTION 2
Given: f ( x )=a x2 −3 x +2
2.1 Determine the value of a if the discriminant of f ( x) is 6. (3)
2.2 Hence, without solving the equation, describe the nature of roots of f (x) (1)
2.3 Determine the numerical value of a for which the roots of f ( x) are equal. (3)
[7]
QUESTION 3
3.1 Simplify the following, without the use of a calculator
0
3.1.1 7(3 x ) (1)
3.1.2 √8 ¿ (3)
n−1 3−2 n
9 × 27
3.1.3 (4)
812−n
3.2 Sove for x : log ( x+2)−log x=1 (4)
3.3 Given the complex number: z=5 – 5 i
3.3.1 Write down the quadrant, in the complex plane, in which z lies. (1)
3.3.1 Express the complex number z in polar form. (4)
3.4 Solve for m and n if m=3 i(2 i – 5)+7 – ∋¿ (4)
[21]
QUESTION 4
4.1 Given the function f and g defined by f ( x )=x 2 + 4 and g ( x )=−2 x+1
4.1.1 Determine the x and y intercepts of f . (3)
4.1.2 Determine the coordinates of the turning point of f (2)
3|Page www.summariessa.co.za Technical Math
Grade 12 June Paper 1
Term 2 - 2024
Paper 1
Total:160 marks Time:2 hours
Learner's name: ________________________________ Gr. 12: __________.
Instructions and information:
This paper consists of five questions, answer all the questions.
You may use a non-programmable and non-graphing calculator.
No Tip – Ex may be used
Show all the steps needed to arrive at the answer.
Good luck!!
Topics covered in this test:
Factoring and solving quadratic equations
Solving linear and non-linear systems of equations
Rearranging formulas
Calculating inductance in an RCL circuit
Conversion between decimal and binary numbers
Quadratic Functions
Nature of Roots
Equal Roots
Simplification and Logarithms
Graphs and Functions
Financial Mathematics
Calculus
Polynomial Functions
Chemical Reaction and Temperature
Integration
1|Page www.summariessa.co.za Technical Math
Grade 12 June Paper 1
,QUESTION 1
1.1 Solve for x
1.1.1 ( 7−3 x ) (−8−x )=0 (2)
2 1
1.1.2 3 x −4 x = (Correct to two decimal places) (4)
3
1.1.3 −x 2+ 16>0 (3)
1.2 Solve for x and y if:
x− y =1 and x +2 xy + y 2 =9 (6)
1.3 In the diagram below shows an RCL circuit used for voltage magnification. The formula to
determine the resonat frequency ( f ¿ of an RCL circuit is given below.
1
f r=
2 π √ LC
Where:
f r=¿resonant frequency in Hz (hertz)
L=¿ inductance in H (henry)
C = capacitance in F (farad)
1.3.1 Make L the subject if the formula. (3)
1.3.2 Hence, calculatee the numerical value of L if C=0.65 ×10−6 F and
f r=1.59 Hz .
(2)
1.4 Express 24 as a binary number. (1)
1.5 Evaluate 144 ÷ 1102 and leave your answer as a decimal number. (2)
[23]
2|Page www.summariessa.co.za Technical Math
Grade 12 June Paper 1
, QUESTION 2
Given: f ( x )=a x2 −3 x +2
2.1 Determine the value of a if the discriminant of f ( x) is 6. (3)
2.2 Hence, without solving the equation, describe the nature of roots of f (x) (1)
2.3 Determine the numerical value of a for which the roots of f ( x) are equal. (3)
[7]
QUESTION 3
3.1 Simplify the following, without the use of a calculator
0
3.1.1 7(3 x ) (1)
3.1.2 √8 ¿ (3)
n−1 3−2 n
9 × 27
3.1.3 (4)
812−n
3.2 Sove for x : log ( x+2)−log x=1 (4)
3.3 Given the complex number: z=5 – 5 i
3.3.1 Write down the quadrant, in the complex plane, in which z lies. (1)
3.3.1 Express the complex number z in polar form. (4)
3.4 Solve for m and n if m=3 i(2 i – 5)+7 – ∋¿ (4)
[21]
QUESTION 4
4.1 Given the function f and g defined by f ( x )=x 2 + 4 and g ( x )=−2 x+1
4.1.1 Determine the x and y intercepts of f . (3)
4.1.2 Determine the coordinates of the turning point of f (2)
3|Page www.summariessa.co.za Technical Math
Grade 12 June Paper 1
